This work deals with dimensioning of wireless mesh networks (WMN) composed of FSO (free space optics) links. Although FSO links realize broadband transmission at low cost, their drawback is sensitivity to adverse weather conditions causing transmission degradation on multiple links. Hence, designing such FSO networks requires an optimization model to find the cheapest configuration of link capacities that will be able to carry an acceptable level of the demanded traffic in all weather states that can be foreseen in network operation. Such a model can be achieved using robust optimization techniques, and for that it is important to find a tractable way of characterizing possible link (capacity) degradation states corresponding to weather conditions not known in advance. In the paper we show how the set of link degradation states may be represented mathematically in a compact and tractable way to be exploited in optimization. To solve this task we will make use of a generalization of a combinatorial problem of finding a minimum hitting set to deduce a compact set approximating a given set of link degradation states, (called uncertainty set). Finally, we provide a mathematical model with respect to a general form of uncertainty sets and illustrate the effectiveness of our model by means of a numerical study.

这项工作涉及由FSO（自由空间光学）链路组成的无线网状网络（WMN）的尺寸确定。尽管FSO链路以低成本实现宽带传输，但它们的缺点是对恶劣天气条件敏感，导致多条链路上的传输性能下降。因此，设计这样的FSO网络需要一个优化模型，以找到链路容量的最便宜的配置，该配置将能够在网络运行中可以预见的所有天气状态下承载可接受水平的需求流量。可以使用鲁棒的优化技术来实现这种模型，为此，重要的是找到一种易于处理的方式来表征与预先未知的天气状况相对应的可能的链路（容量）退化状态。在本文中，我们展示了如何以紧凑而易于处理的方式数学地表示一组链路退化状态，以便在优化中加以利用。为了解决该任务，我们将利用组合问题的一般化，即找到最小的击中集来推导紧凑的集合，该集合逼近给定的一组链路退化状态（称为不确定性集合）。最后，我们针对不确定性集的一般形式提供了数学模型，并通过数值研究说明了模型的有效性。